Use the formula given in Exercise 94 to demonstrate that the distance from the point (x0...

Use the formula given in Exercise 94 to demonstrate that the distance from the point (x₀, y₀) to the line Ax + By + C = 0 is

Reference

In this exercise you’ll derive a useful formula for the (perpendicular) distance d from the point (x₀, y₀) to the line y = mx + b. The formula is

(a) Refer to the figure. Use similar triangles to show that

Therefore

(b) Check that

(c) Conclude from parts (a) and (b) that

For the general case (in which the point and line may not be situated as in our figure), we need to use the absolute value of the quantity in the numerator to ensure that AB and d are nonnegative.